This communication in uences on magnetohydrodynamic ow of viscoelastic uid with magnetic  eld induced by oscillating plate. General solutions have been found out for velocity and shear stress pro les using mathematical transformations (integral transforms). The governing partial di erential equations have been solved analytically under boundary conditions u(0; t) = A0H(t)sin( t) and u(0; t) = A0H(t)cos( t) with t  0. For the sake of simplicity of boundary conditions are veri ed on the analytical general solutions and similar solutions have been particularized under three limited cases namely (i) Maxwell uid without magnetic  eld if 6= 0; M = 0 (ii) Newtonian uid with magnetic  eld if = 0; M 6= 0 and (iii) Newtonian uid with out magnetic  eld if = 0; M = 0. Finally various physical parameters with variations of uid behaviors are analyzed and depicted graphical illustrations.

The present paper aims at investigating the manner of two dissipative massive scalar  elds. Two massive scalar  elds that interact with a reservoir were con-sidered and a reservoir was modeled by continuum Klein-Gordon  elds. The Lagrangian of the total system was canonically quantized and the dynamics of the system was de-termined using the Euler-Lagrange equation. Then, the explicit form of the quantum massive scalar  elds in long-time limit were observed. The propagator of the system and correlation functions were calculated at  nite temperature in the thermo eld dynamics formalizem.

One of the most important parameters in designing sewer structures is the ability to accurately simulate their discharge and velocity  eld. Among the various sewer receiving in ow methods, open-channel junctions are the most frequently utilized ones. Because of the existence of separation and contraction zones in the open-channel junctions, the uid ow has a complex behavior. Modeling is carried out by Radial Basis Function (RBF) neural network, Gene Expression Programming (GEP), and Multiple Non-Linear Regression (MNLR) methods. Finding the optimum situation for GEP and RBF models is done by examining various mathematical and linking functions for GEP, di erent numbers of hidden neurons, and various spread amounts for RBF. In order to use the models in practical situations, three equations were conducted by using the RBF, GEP, and MNLR methods in modeling the longitudinal velocity. Then, the surface integral of the presented equations was used to simulate the ow discharge. The results showed that the GEP and RBF methods performed signi cantly better than the MNLR in open-channel junction characteristics simulations. The GEP method had better performance than the RBF in modeling the longitudinal velocity  eld. However, the RBF presented more reliable results in the discharge simulations.

In this article, we studied the peristaltic motion of Jeffrey fluid with porous medium through an asymmetric channel under the influence of velocity slip parameters. Governing equations for non-Newtonian fluid flow models such as continuity, momentum, energy and mass transfer equations are formulated. Externally applied inclined magnetic field is also considered in the flow pattern. The lengthy governing equation of fluid motion is reduced by taking into the account of approximation of longer wavelengths and smaller Reynolds numbers The resulting governing equations are solved exactly. The graph shows the results of the impact of various related fluid parameters such as Hartmann number, Darcy number, Jeffrey fluid parameter, amplitude ratio, chemical reactions of fluid velocity, temperature, concentration, pressure rise, pressure gradient, streamlines etc. Finally, the various waveforms of the trapping phenomenon are presented.

This study presents the characteristics of Cattaneo-Christov heat ux model for the boundary layer ow of Burgers' uid model. Instead of simple Fourier's law of heat conduction, we presented the Cattaneo-Christov model to analyze the thermal relaxation properties when the heat source/sink was present in the system. Mathematical modeling of the laws of momentum and energy were presented under the order analysis approach. It was revealed that the term \ B2 0u= " was for the hydro-magnetic rheology of the Newtonian model whereas the generalized magnetic  eld term was for the Burgers' model, which was incorporated in the current analysis. Suitable transformations were utilized for the conversion of partial di erential system into coupled nonlinear set of ordinary di erential equations, which was tackled analytically through homotopy analysis technique. The plots of various physical quantities are presented, showing the dynamics of the considered analysis. Streamlines for Burgers' and Newtonian models are presented, which show their di erence in rheology. Numerical values for skin friction and surface heat transfer rate are presented in tables.

The navigation technique is very e, ective to obtain or classify a Finsler metric from a given a Finsler metric (especially a Riemannian metric) under an action of a vector , eld on a di, erential manifold. In this survey, we will survey some recent progress on the navigation problem and conformal vector , elds on Finsler manifolds, and their applications in the classi, cations of some Finsler metrics of scalar (resp. constant) ag curvature.

The phenomenon of defectless extensions is a classical notion in the framework of valued  elds and valued vector spaces in valuation theory. The aim of this paper is to study various results regarding this concept and its applications.

One of the most useful tools for handling multivariate distributions of de-pendent variables in terms of their marginal distribution is a copula function. The copula families capture a fair amount of attention due to their applicability and exibil-ity in describing the non-Gaussian spatial dependent data. The particular properties of the spatial copula are rarely seen in all the known copula families. In the present paper, based on the weighted geometric mean of two Max-id copulas family, the spatial copula function is provided. Afterwards, the proposed copula along with the Bees algorithm is used to explore the spatial dependency and to interpolate the rainfall data in Iran's Khuzestan province.